Understanding Linear Functions

This video tutorial explains how to determine if a table of values represents a linear function by calculating the rate of change between points. It covers the concept of slope as a constant rate of change and provides examples to verify linearity. The tutorial also demonstrates how to identify non-linear functions and verify results graphically.

What is the rate of change between two points generally defined as?

• The change in input divided by the change in output

• The sum of the outputs divided by the sum of the inputs

• The product of the outputs and inputs

• The change in output divided by the change in input

What is the significance of the Greek letter delta in the context of rate of change?

• It represents the sum of values

• It denotes the change in values

• It signifies the average of values

• It indicates the product of values

How can you determine if a function is linear?

• By plotting the points and checking if they form a circle

• By checking if the rate of change is different for each pair of points

• By ensuring the rate of change is constant between any pair of points

• By calculating the sum of all outputs

In the context of linear functions, what does a constant rate of change imply?

• The function is logarithmic

• The function is quadratic

• The function is exponential

• The function is linear

In the example provided, what was the constant rate of change that indicated a linear function?

• 12

• 10

• 8

• 15

What does a non-linear function's rate of change look like?

• It is always zero

• It is always negative

• It varies between different pairs of points

• It remains constant

In the non-linear example, what was the rate of change between the first two points?

• 9

• 17

• 23

• 35

What was the slope of the linear function in the final example?

• -8

• -12

• 12

• 8

How can you graphically verify a linear function?

• By ensuring all points lie on the x-axis

• By plotting points and checking if they form a curve

• By ensuring all points lie on the y-axis

• By plotting points and checking if they form a straight line

What was the rate of change between the last two points in the final example?

• 8

• -12

• -8

• 12